Generation of ultra-long pure magnetization needle and multiple spots by phase modulated doughnut Gaussian beam

•Phase modulated azimuthally polarized doughnut Gaussian beam is studied.•Focusing properties are investigated theoretically by vector diffraction theory.•Intensity distribution in focal region plays an important role in optical systems.•We can generating smallest focal spot and multiple spots intensity profiles.•Its find many applications in multiple trapping of magnetic particles. Based on vector diffraction theory and inverse Faraday effect (IFE), the light induced magnetization distribution of a tightly focused azimuthally polarized doughnut Gaussian beam superimposed with a helical phase and modulated by an optimized multi belt complex phase filter (MBCPF) is analysed numerically. It is noted that by adjusting the radii of different rings of the complex phase filter, one can achieve many novel magnetization focal distribution such as sub wavelength scale (0.29λ) and super long (52.2λ) longitudinal magnetic probe suitable for all optical magnetic recording and the formation of multiple magnetization chain with four, six and eight sub-wavelength spherical magnetization spots suitable for multiple trapping of magnetic particles are achieved.